Unconventional Ferroelectric Transition in the Multiferroic Compound TbMnO3 Revealed by the Absence of an Anomaly in c-Polarized Phonon Dispersion

TbMnO3 exhibits a spontaneous electric polarization along c concomitantly with a spiral spin ordering modulated along b below T-C=28 K. We have performed inelastic x-ray scattering measurements on a single crystal of TbMnO3 to clarify whether phonon anomalies related to the ferroelectricity exist. We measured transverse modes, especially the Mn-O-Mn bending mode polarized along c and propagating along b, which we expect is most relevant to the ferroelectricity. However, no anomaly was found in the phonon dispersion below 50 meV across T-C. The present result suggests that the mechanism of ferroelectricity in TbMnO3 is different from that of a conventional displacive-type ferroelectric. The weak coupling between electric polarization and lattice in TbMnO3 strongly suggests that the ferroelectricity is mainly derived from the spiral spin ordering.